On approximation properties of functions by means of Fourier and Faber series in weighted Lebesgue spaces with variable exponent

Sadulla Z. Jafarov

In this paper the approximation of functions by linear means of Fourier series in weighted variable exponent Lebesgue spaces was studied. This result was applied to the approximation of the functions by linear means of Faber series in Smirnov classes with variable exponent defined on simply connected domain of the complex plane.